Exploring instantons in nonlinear sigma models with spin-lattice systems

Instanton processes are present in a variety of quantum field theories relevant to high energy as well as condensed matter physics. While they have led to important theoretical insights and physical applications, their underlying features often remain elusive due to the complicated computational treatment. Here, we address this problem by studying topological as well as nontopological instantons using Monte Carlo methods on lattices of interacting spins. As a proof of principle, we systematically construct instanton solutions in O(3) nonlinear sigma models with a Dzyaloshinskii-Moriya interaction in (1 + 1) and (1 + 2) dimensions, thereby resembling an example of a chiral magnet. We demonstrate that, due to their close correspondence, Monte Carlo techniques in spin-lattice systems are well suited to describe topologically nontrivial field configurations in these theories. In particular, by means of simulated annealing, we demonstrate how to obtain domain walls, merons, and critical instanton solutions.

Automated summary

Instanton processes are studied using Monte Carlo methods on lattices of interacting spins to address the elusive features of these processes in quantum field theories. Instanton solutions in O(3) nonlinear sigma models with Dzyaloshinskii-Moriya interaction in (1 + 1) and (1 + 2) dimensions are systematically constructed, demonstrating the suitability of Monte Carlo techniques in describing topologically nontrivial field configurations in these theories. Simulated annealing is used to obtain domain walls, merons, and critical instanton solutions.